[[HARD - Polynomials]] Consider the curve y = x^5 - 10x^4 + 22x^3 + 32x^2 - 20x + 20. Find the equation of the line which intersects the curve at (-2, -180) and is a tangent to the curve at two other points.

Question

toxicsugar22 · Answer

Modulas can u help me after her

toxicsugar22 · Answer

please

anonymous · Answer

Take derivative, find zeros, then find the points of those zeros in the original equation. When you have the points (there shouldn't be too many) find which 2 make a line that intersects the given point.

anonymous · Answer

or actually nm, those zeros wont work because the slope of the line you need isn't going to be 0

anonymous · Answer

mm. I differentiated y, but I don't know what to do with the differential.
I let the line be y = mx + b and set 
x^5 - 10x^4 + 22x^3 + 32x^2 - 20x + 20 = mx + b
Kindda stuck after that

anonymous · Answer

You need a slope around x = 5 and .5 that is the same. But how to get that I'm not sure.

anonymous · Answer

and if that is the derivative, the derivative should = m since it will serve as the slope

anonymous · Answer

I gtg though, gl with it

anonymous · Answer

alright, thanks.